is symmetric and positive definite (see [1]} in general). In particular, \(P\)  and \(Q\)  are themselves symmetric and positive definite.
As for \(R\)  and \(R^T\)  we need to be explicit with what are row and column indices above: in all entries above,
\(k\)  is the row index, \(j\)  the column index. Thus, for example, \(R_{kj}=\oint _{\beta _k}*dU_{\alpha _j}\) .
